Shear Stress Given Shear Strain Energy Calculator

Shear Stress Formula:

\[ \tau = \sqrt{\frac{U \times 2 \times G}{V}} \]

Strain Energy in body (U):

Joule

Modulus of rigidity of Shaft (G):

Pascal

Volume of Shaft (V):

Cubic Meter

Shear stress on surface of shaft (τ):

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1. What is Shear Stress Given Shear Strain Energy?

Shear stress on the surface of a shaft is the force tending to cause deformation of a material by slippage along a plane or planes parallel to the imposed stress. This calculator determines shear stress based on strain energy stored in the body.

2. How Does the Calculator Work?

The calculator uses the shear stress formula:

\[ \tau = \sqrt{\frac{U \times 2 \times G}{V}} \]

Where:

\( \tau \) — Shear stress on surface of shaft (Pascal)
\( U \) — Strain Energy in body (Joule)
\( G \) — Modulus of rigidity of Shaft (Pascal)
\( V \) — Volume of Shaft (Cubic Meter)

Explanation: The formula calculates shear stress by considering the relationship between strain energy, material rigidity, and the volume of the shaft under torsion.

3. Importance of Shear Stress Calculation

Details: Accurate shear stress calculation is crucial for designing mechanical components, assessing material strength, and ensuring structural integrity under torsional loads.

4. Using the Calculator

Tips: Enter strain energy in joules, modulus of rigidity in pascals, and volume in cubic meters. All values must be positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is strain energy in a body?
A: Strain energy is defined as the energy stored in a body due to deformation when subjected to external forces.

Q2: What is modulus of rigidity?
A: Modulus of rigidity is the elastic coefficient when a shear force is applied resulting in lateral deformation. It measures how rigid a material is.

Q3: When should this calculation be used?
A: This calculation is particularly useful for cylindrical shafts and components under torsion where shear stress distribution needs to be determined.

Q4: Are there limitations to this formula?
A: This formula assumes homogeneous material properties and may have limitations for complex geometries or non-uniform stress distributions.

Q5: What units should be used for input values?
A: Use consistent SI units: joules for energy, pascals for modulus of rigidity, and cubic meters for volume to get results in pascals.